Question: Solve for $s$. $2-2s=\dfrac34s+13$ $s=$
Answer: We need to manipulate the equation to get $ s $ by itself. 2 − 2 s 2 − 2 s − 3 4 s − 11 4 s + 2 − 11 4 s + 2 − 2 − 11 4 s − 11 4 s ⋅ ( − 4 11 ) s s = 3 4 s + 13 = 3 4 s + 13 − 3 4 s = 13 = 13 − 2 = 11 = 11 ⋅ ( − 4 11 ) = − 44 11 = − 4 Subtract 3 4 s from each side. Combine like terms. Subtract 2 from each side. Combine like terms. Multiply each side by - 4 11. Simplify. \begin{aligned} 2-2s&=\dfrac34s+13 \\\\ 2-2s {-\dfrac34s} &= \dfrac34s+13{-\dfrac34s} &&\gray{\text{Subtract }\dfrac34s \text{ from each side.}}\\\\ -\dfrac{11}4 s+2&=13 &&\gray{\text{Combine like terms.}}\\\\ -\dfrac{11}4s+2{-2} &= 13{-2} &&\gray{\text{Subtract 2 from each side.}}\\\\ -\dfrac{11}4s &=11 &&\gray{\text{Combine like terms.}}\\\\ -\dfrac{11}{4}s\cdot\left({-\dfrac{4}{11}}\right) &= 11\cdot\left({-\dfrac{4}{11}}\right) &&\gray{\text{Multiply each side by -}\dfrac{4}{11}.}\\\\ s&=-\dfrac{44}{11}\\\\\ s &= {-4} &&\gray{\text{Simplify.}}\\\\ \end{aligned} The answer: $s = { -4 }~~~~~~~~$ [Let's check our work!]